Score : $200$ points

问题描述

高桥正在开发一款RPG游戏。他决定编写一段代码来检查两个地图是否相等。

我们有网格 $A$ 和 $B$，它们都有 $H$ 行和 $W$ 列。每个格子上都写有一个符号#或.。

在网格 $A$ 和 $B$ 中，从上到下第 $i$ 行、从左到右第 $j$ 列的格子上的符号分别表示为 $A_{i, j}$ 和 $B_{i, j}$。

以下两种操作被称为垂直平移和水平平移。

• 对于所有 $j=1, 2, \dots, W$ 同时执行以下操作：
  • 同时将 $A_{1,j}, A_{2,j}, \dots, A_{H-1, j}, A_{H,j}$ 替换为 $A_{2,j}, A_{3,j}, \dots, A_{H,j}, A_{1,j}$。
• 对于所有 $i = 1, 2, \dots, H$ 同时执行以下操作：
  • 同时将 $A_{i,1}, A_{i,2}, \dots, A_{i,W-1}, A_{i,W}$ 替换为 $A_{i, 2}, A_{i, 3}, \dots, A_{i,W}, A_{i,1}$。

是否存在一对非负整数 $(s, t)$ 满足以下条件？如果存在则输出 Yes，否则输出 No。

• 应用 $s$ 次垂直平移和 $t$ 次水平平移后，$A$ 等于 $B$。

这里，若对于所有满足 $1 \leq i \leq H$ 和 $1 \leq j \leq W$ 的整数对 $(i, j)$，均有 $A_{i, j} = B_{i, j}$，则称 $A$ 等于 $B$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is developing an RPG. He has decided to write a code that checks whether two maps are equal.

We have grids $A$ and $B$ with $H$ horizontal rows and $W$ vertical columns. Each cell in the grid has a symbol # or . written on it.
The symbols written on the cell at the $i$-th row from the top and $j$-th column from the left in $A$ and $B$ are denoted by $A_{i, j}$ and $B_{i, j}$, respectively.

The following two operations are called a vertical shift and horizontal shift.

• For each $j=1, 2, \dots, W$, simultaneously do the following:
  • simultaneously replace $A_{1,j}, A_{2,j}, \dots, A_{H-1, j}, A_{H,j}$ with $A_{2,j}, A_{3,j}, \dots, A_{H,j}, A_{1,j}$.
• For each $i = 1, 2, \dots, H$, simultaneously do the following:
  • simultaneously replace $A_{i,1}, A_{i,2}, \dots, A_{i,W-1}, A_{i,W}$ with $A_{i, 2}, A_{i, 3}, \dots, A_{i,W}, A_{i,1}$.

Is there a pair of non-negative integers $(s, t)$ that satisfies the following condition? Print Yes if there is, and No otherwise.

• After applying a vertical shift $s$ times and a horizontal shift $t$ times, $A$ is equal to $B$.

Here, $A$ is said to be equal to $B$ if and only if $A_{i, j} = B_{i, j}$ for all integer pairs $(i, j)$ such that $1 \leq i \leq H$ and $1 \leq j \leq W$.

Constraints

• $2 \leq H, W \leq 30$
• $A_{i,j}$ is # or ., and so is $B_{i,j}$.
• $H$ and $W$ are integers.

Input

The input is given from Standard Input in the following format:

$H$ $W$

$A_{1,1}A_{1,2}\dots A_{1,W}$

$A_{2,1}A_{2,2}\dots A_{2,W}$

$\vdots$

$A_{H,1}A_{H,2}\dots A_{H,W}$

$B_{1,1}B_{1,2}\dots B_{1,W}$

$B_{2,1}B_{2,2}\dots B_{2,W}$

$\vdots$

$B_{H,1}B_{H,2}\dots B_{H,W}$

Output

Print Yes if there is a conforming integer pair $(s, t)$; print No otherwise.

Sample Input 1

4 3
..#
...
.#.
...
#..
...
.#.
...

Sample Output 1

Yes

By choosing $(s, t) = (2, 1)$, the resulting $A$ is equal to $B$.
We describe the procedure when $(s, t) = (2, 1)$ is chosen. Initially, $A$ is as follows.

..#
...
.#.
...

We first apply a vertical shift to make $A$ as follows.

...
.#.
...
..#

Then we apply another vertical shift to make $A$ as follows.

.#.
...
..#
...

Finally, we apply a horizontal shift to make $A$ as follows, which equals $B$.

#..
...
.#.
...

Sample Input 2

3 2
##
##
#.
..
#.
#.

Sample Output 2

No

No choice of $(s, t)$ makes $A$ equal $B$.

Sample Input 3

4 5
#####
.#...
.##..
..##.
...##
#...#
#####
...#.

Sample Output 3

Yes

Sample Input 4

10 30
..........##########..........
..........####....###.....##..
.....##....##......##...#####.
....####...##..#####...##...##
...##..##..##......##..##....#
#.##....##....##...##..##.....
..##....##.##..#####...##...##
..###..###..............##.##.
.#..####..#..............###..
#..........##.................
................#..........##.
######....................####
....###.....##............####
.....##...#####......##....##.
.#####...##...##....####...##.
.....##..##....#...##..##..##.
##...##..##.....#.##....##....
.#####...##...##..##....##.##.
..........##.##...###..###....
...........###...#..####..#...

Sample Output 4

Yes

update @ 2024/3/10 08:23:16